{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 从0实现线性回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from d2l import torch as d2l\n",
    "def synthetic_data(w, b, num_examples): #@save\n",
    "    \"\"\"生成y=Xw+b+噪声\"\"\"\n",
    "    X = torch.normal(0, 1, (num_examples, len(w)))#X有w长度的列，有样本数量的行\n",
    "    y = torch.matmul(X, w) + b\n",
    "    y += torch.normal(0, 0.01, y.shape)#添加噪声\n",
    "    return X, y.reshape((-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "true_w = torch.tensor([2, -3.4])\n",
    "true_b = 4.2\n",
    "features, labels = synthetic_data(true_w, true_b, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "features: tensor([-0.6427, -1.1662]) \n",
      "label: tensor([6.8816])\n"
     ]
    }
   ],
   "source": [
    "print('features:', features[0],'\\nlabel:', labels[0])#分别是X与y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "#两者的线性关系\n",
    "d2l.set_figsize()\n",
    "d2l.plt.scatter(features[:, (1)].detach().numpy(), labels.detach().numpy(), 1);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "读取数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))#将索引乱序，保证泛化能力\n",
    "    # 这些样本是随机读取的，没有特定的顺序\n",
    "    random.shuffle(indices)\n",
    "    for i in range(0, num_examples, batch_size):#索引从第0行数据到最终的数据，步长为批次\n",
    "        \"\"\"\n",
    "        取出i到i+batch_size的索引并且确保不超过num_examples的范围\n",
    "        \"\"\"\n",
    "        batch_indices = torch.tensor(indices[i: min(i + batch_size, num_examples)])\n",
    "        yield features[batch_indices], labels[batch_indices]#返回一批又一批的数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 2.3402,  1.1248],\n",
      "        [-1.3488,  0.6513],\n",
      "        [-0.5686,  0.0941],\n",
      "        [ 0.7610,  0.4971],\n",
      "        [ 1.3483, -1.1039],\n",
      "        [-0.1666, -0.5583],\n",
      "        [-1.4319,  1.1768],\n",
      "        [ 0.7670,  1.2071],\n",
      "        [-1.2931,  0.2546],\n",
      "        [-0.0891, -0.6947]]) \n",
      " tensor([[ 5.0393],\n",
      "        [-0.7030],\n",
      "        [ 2.7250],\n",
      "        [ 4.0263],\n",
      "        [10.6673],\n",
      "        [ 5.7586],\n",
      "        [-2.6717],\n",
      "        [ 1.6142],\n",
      "        [ 0.7455],\n",
      "        [ 6.3980]])\n"
     ]
    }
   ],
   "source": [
    "#就打印一批\n",
    "batch_size = 10\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "    print(X, '\\n', y)\n",
    "    break"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "初始化参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "w=torch.normal(0,0.01,size=(2,1),requires_grad=True)#每一行x数据是1x2，所以特征w初始化是2X1\n",
    "b=torch.zeros(1,requires_grad=True)\n",
    "#接下来不断优化w和b"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linreg(X, w, b): #@save\n",
    "    \"\"\"线性回归模型\"\"\"\n",
    "    return torch.matmul(X, w) + b"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def squared_loss(y_hat, y): #@save\n",
    "    \"\"\"均方损失\"\"\"\n",
    "    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "优化算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sgd(params, lr, batch_size): #@save\n",
    "    \"\"\"小批量随机梯度下降\"\"\"\n",
    "    with torch.no_grad():#在这个代码块中(torch.no_grad())不进行梯度计算\n",
    "        for param in params:\n",
    "            param -= lr * param.grad / batch_size\n",
    "            param.grad.zero_()#梯度清0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "#超参数设置，后续会教怎么调\n",
    "lr = 0.03\n",
    "num_epochs = 3\n",
    "net = linreg\n",
    "loss = squared_loss"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "训练"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.030386\n",
      "epoch 2, loss 0.000099\n",
      "epoch 3, loss 0.000045\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(num_epochs):\n",
    "    for X, y in data_iter(batch_size, features, labels):\n",
    "        l = loss(net(X, w, b), y) # X和y的小批量损失\n",
    "        # 因为l形状是(batch_size,1)，而不是一个标量。l中的所有元素被加到一起，\n",
    "        # 并以此计算关于[w,b]的梯度\n",
    "        l.sum().backward()\n",
    "        sgd([w, b], lr, batch_size) # 使用参数的梯度更新参数\n",
    "    with torch.no_grad():\n",
    "        train_l = loss(net(features, w, b), labels)#计算损失值\n",
    "        print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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